Existence of a principal eigenvalue for the Tricomi problem

Daniela Lupo & Kevin R. Payne
Abstract:
The existence of a principal eigenvalue is established for the Tricomi problem
in normal domains; that is, the existence of a positive
eigenvalue of minimum modulus with an associated positive eigenfunction.
The argument here uses prior results of the authors on the generalized
solvability in weighted Sobolev spaces and associated
maximum/minimum principles [17] coupled with known results
of Krein-Rutman type.